Frequently Asked Questions

Q.  Historically Math 5451 used to be part of a three quarter sequence Math 601-602-701, now Math 5101-5102-5451
      in the semester environment.
       Is it necessary that one take Math 5451 as the last course in such a sequence?

A.  No. The instructor's objective has been to make Math 5451 pretty much self-contained. In fact, in the past
      there have been students who have taken this course before Math 5101 however, these students were
      already familiar with the prerequisites or they simply worked harder than the others.

Q.  Why should (a) engineers, (b) physicists, (c) mathematicians take Math 5451?

A.  Math 5451 occupies a prominent  and natural role in the  engineering arts,  in physics,  in mathematics, etc.

      (a)  In the engineering arts optimization processes on infinite dimensional parameter spaces and their
             finite dimensional approximations,  open new conceptual vistas which would remain inaccessible
             within the framework of finite-dimensional calculus.

      (b)  In physics Math 5451 furnishes, among others, very powerful extremum principles. By cutting across
             diverse aspects of nature, these principles allow, for example,  a grasp of classical and wave mechanics
             from a single perspective and with respect to any coordinate frame.

      (c)  For mathematics Math 5451 provides a natural  connecting link between  theoretical mathematics 
            (e.g. global analysis, differential geometry, etc.) and its foundational roots in applied mathematics
            (e.g. classical and wave mechanics, covariant differentiation, etc.)